• Proceedings of the KSME Conference
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• 2000.04a
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• pp.894-899
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• 2000

An automatic mesh generation system with unstructured quadrilateral elements on trimmed NURBS surfaces has been developed.. In this paper, NURBS surface geometries in the IGES format have been used to represent model shape. NURBS surface is represented as parametric surface. So each surface could be mapped to a 2D parametric plane through the parametric domain. And then meshes with quadrilateral elements are constructed in this plane. Finally, the constructed meshes are mapped back to the original 3D surface through the parametric domain. In this paper, projection plane, quasi-expanded plane and parametric Plane are used as 2D mesh generation plane. For mapping 3D surface to parametric domain, Newton-Rhapson Method is employed. For unstructured mesh generation with quadrilateral elements on 2D plane, a domain decomposition algorithm using loop operators has been employed. Sample meshes are represented to demonstrate the effectiveness of the proposed algorithm.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1411-1429
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• 2016

We consider the nite volume element method for elliptic problems using isoparametric bilinear elements on quadrilateral meshes. A gradient recovery method is presented by using the patch interpolation technique. Based on some superclose estimates, we prove that the recovered gradient $R({\nabla}u_h)$ possesses the superconvergence: ${\parallel}{\nabla}u-R({\nabla}u_h){\parallel}=O(h^2){\parallel}u{\parallel}_3$. Finally, some numerical examples are provided to illustrate our theoretical analysis.

• Magazine of the Korean Society of Agricultural Engineers
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• v.37 no.2
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• pp.21-30
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• 1995

In order to save time and efforts in generating finite element meshes in irregular houndaries of domains, it is needed to develop an automatic mesh-generator which can hoth promote the accuracy of solutions and reduce the run-time in operating finite ele- ment models. In this study, the advancing front technique of triangular mesh generation and the transforming technique from triangular meshes to quadrilateral meshes were used to de- velop a computer program for the automatic triangular and quadrilateral meshes in the mixed shape. Furthermore, to enhance the quadrilateral mesh quality, the techniques of Laplancian smoothing and interior mesh modification were employed. The mesh genera- tor was applied to evaluate its applicability to irregular and complex geometries such as Nakdong river bay. In has hoen shown that the automatic mesh generator developed is capable of automatically generating meshes for irreguiar and complex geometries with high qualities of meshes and with the simple input data of arbitrarily specified nodal spacing in bound- aries.

• Korean Journal of Computational Design and Engineering
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• v.4 no.2
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• pp.153-161
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• 1999

An atomatic mesh generation scheme with unstructured quadrilateral elements on trimmed surfaces has been developed. Trimmed surfaces are often encountered in modeling of structures with complex shapes such as aircrafts, automobile structures, pressure vessels and etc. For unstructured mesh generation with quadrilateral elements, a domain decomposition algorithm employing loop operators has been used. Mesh generation on trimmed surface is performed in three steps. First, trimmed surfaces with holes or cuts are transformed to th largest projection planes in which the meshes are constructed. The constructed meshes are transformed to the u-v parametric plane and then finally to the original 3D surfaces. Th exact locations of holes or cuts in projection planes are determined by the Newton-Raphson method. Sample meshes are constructed to demonstrate the effectiveness of the proposed algorithm.

• International Journal of CAD/CAM
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• v.1 no.1
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• pp.11-21
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• 2002

This paper presents a triangular-to-quadrilateral mesh conversion method that can control the directionality of the output quadrilateral mesh according to a user-specified vector field. Given a triangular mesh and a vector field, the method first scores all possible quadrilaterals that can be formed by pairs of adjacent triangles, according to their shape and directionality. It then converts the pairs into quadrilateral elements in order of the scores to form a quadrilateral mesh. Engineering analyses with finite element methods occasionally require a quadrilateral mesh well aligned along the boundary geometry or the directionality of some physical phenomena, such as in the directions of a streamline, shock boundary, or force propagation vectors. The mesh conversion method can control the mesh directionality according to any desired vector fields, and the method can be used with any existing triangular mesh generators.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.949-958
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• 2022

The aim of this papaer is to prove the discrete compactness property for modified Raviart-Thomas element(MRT) of lowest order on quadrilateral meshes. Then MRT space can be used for eigenvalue problems, and is more efficient than the lowest order ABF space since it has less degrees of freedom.

• Transactions of the Korean Society of Automotive Engineers
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• v.3 no.6
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• pp.145-153
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• 1995

An algorithm for the automatic generation of quadrilateral shell elements on three-dimensional sculptured surfaces has been developed, which is one of the key issues in the finite element analysis of structures with complex shapes such as automobile structures. Mesh generation on sculptured surfaces is performed in three steps. First a sculptured surface is transformed to a projection plane, on which the loops are subdivided into subloops by using the best split lines, and with the use of 6-node/8-node loop operators and a layer operator, quadrilateral finite elements are constructed on this plane. Finally, the constructed mesh is transformed back to the original sculptured surfaces. The proposed mesh generation scheme is suited for the generation of non-uniform meshes so that it can be effectively used when the desired mesh density is available. Sample meshes are presented to demonstrate the versatility of the algorithm.

• Journal of Mechanical Science and Technology
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• v.15 no.5
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• pp.592-601
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• 2001

An automatic mesh generation scheme with unstructured quadrilateral elements on trimmed NURBS surfaces has been developed. In this paper NURBS surface geometries in the IGES format have been employed to represent geometric models. For unstructured mesh generation with quadrilateral elements, a domain decomposition algorithm employing loop operators has been modified. As for the surface meshing, an indirect 2D approach is proposed in which both quasi-expanded planes and projection planes are employed. Sampled meshes for complex models are presented to demonstrate the robustness of the algorithm.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.12
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• pp.2995-3006
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• 1993

An automatic mesh generation scheme has been developed for finite element analysis with two-dimensional, quadrilateral elements. The basic strategies of the method are to transform the analysis domain into loops with key nodes and the loops are recursively subdivided into subloops with the use of best split lines. Finally by using the basic loop operators, the meshes are completed. In this algorithm an eight-node loop operator is proposed, which is useful in the area where the change of element size is large and the splitting criteria for subdividing the loops have also been modified to the existing algorithms. Lines, arcs, and cubic spline curves are used to define the boundaries of analysis domain. Sample meshes for several geometries are presented to demonstrate the robustness of the algorithm.

• Korean Journal of Computational Design and Engineering
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• v.11 no.2
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• pp.107-114
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• 2006

A new quadrilateral mesh generation technique from an existing triangle mesh is proposed in this paper. The proposed method is based on advancing front method and zero-thickness layer. Beginning with an initial triangular mesh, boundary triangular elements are removed and quadrilateral elements with zero thickness are generated. A quality of quadrilateral elements is improved during a mesh smoothing process. Until all initial triangular elements are removed, this procedure is repeated. Sample meshes are constructed to demonstrate the mesh generation capability of proposed algorithm.